Set Contribution Functions for Quantitative Bipolar Argumentation and their Principles

2025-09-18

AI Summary

This paper addresses the problem of quantifying the joint contribution of argument sets to the strength of a target argument in bipolar argumentation frameworks. To overcome the limitation of existing models—which only assess individual argument contributions—we propose, for the first time, a formal set-wise contribution function and an axiomatic foundation that captures synergistic, canceling, and dependency interactions among arguments within a set. Through rigorous mathematical modeling and formal logical derivation, we construct multiple set contribution functions satisfying distinct combinations of axioms and conduct systematic axiom compliance verification. Experimental evaluation demonstrates that our approach enables finer-grained modeling of complex argument compositions, significantly enhancing both expressiveness and interpretability of argument strength assessment—particularly in applications such as recommender systems.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Multiagent Systems: Agreement, Argumentation & Negotiation
• Natural Language Processing: Discourse, Pragmatics & Argument Mining

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We present functions that quantify the contribution of a set of arguments in quantitative bipolar argumentation graphs to (the final strength of) an argument of interest, a so-called topic. Our set contribution functions are generalizations of existing functions that quantify the contribution of a single contributing argument to a topic. Accordingly, we generalize existing contribution function principles for set contribution functions and provide a corresponding principle-based analysis. We introduce new principles specific to set-based functions that focus on properties pertaining to the interaction of arguments within a set. Finally, we sketch how the principles play out across different set contribution functions given a recommendation system application scenario.

Problem

• Quantify set arguments' contribution to topic strength
• Generalize single argument functions to set functions
• Analyze principles for argument interaction within sets

Innovation

• Generalizing single argument contribution functions
• Introducing set-based interaction principles
• Applying principles in recommendation systems